Step 1:
\The function is .
Differentiate with respect to .
Find the critical number by equating to zero.
Roots of the quadratic equation are
.
Compare with
.
Substitute corresponding values in the
.
Step 2:
\Critical points are .
Split the critical number in to three intervals as
Interval | \Test Value | \Sign of ![]() | \
Conclusion | \
![]() | \
![]() | \
\
\ | \
Increasing | \
![]() | \
![]() | \
\
\ | \
Decreasing | \
![]() | \
![]() | \
\
\ | \
Increasing | \
Thus, the function is increasing on the interval and
.
And decreasing on the interval .
Solution:
\The function is increasing on intervals
and
\
\
\
\